The Greek philosopher Heraclitus stated that the “only thing that is constant is change.” However, meaningful change rarely unfolds in straight lines but typically follow the Sigmoid Curve (S-fxn) shape of the power law. The ‘slow, fast, slow’ structure of the curve describes a vast range of natural and historical phenomenon. Stephen J. Gould’s description of evolution in the form of punctuated equilibrium, Joseph Schumpeter’s creative destruction, and Thomas Kuhn’s paradigm shifts in science can all be explained by S-curves. The S-fxn is intimately related to the Gaussian curve via a differential. The “slow, fast, slow” of the sigmoid curve becomes the “low, high, low” of the bell curve. The universe is filled with S-curves, however, the nature of the relationship makes them mostly invisible to us. In a phase transition, an event is more surprising the longer we have been waiting for it, and maximally surprising, right before it happens.
On a personal level, learning, skill building, expertise development all follow the S curve – slow, fast, slow. We plod along in the initial slow phase with the following framework:
- Setting clear, well-defined goals that are sufficiently challenging but also realistic and attainable
- Developing a plan to achieve the goal and become immersed in the activity to achieve the goal.
- Constantly measuring progress with appropriate metrics and readjusting the goal when milestones are met.
- Sustaining involvement by wholeheartedly committing to the goal and concentrating on the task. It is the depth of involvement in the activity that will remove distractions and keep the involvement sustainable.
Then voila, in a blink of an eye and without warning, insight is gained and we emerge with new symmetries of a phase transition. In French, the verb essayer means to try, to attempt, to embark upon. I hope to use these essays for personal growth in the search for phase transitions. As the historian, Will Durant so eloquently stated, “the only real revolution is in the enlightenment of the mind and the improvement of character, the only real emancipation is individual.”